--- manual/s_overview/text/manual.tex	2004/03/23 16:47:04	1.19
+++ manual/s_overview/text/manual.tex	2006/06/28 15:22:13	1.26
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 %tci%\documentclass[12pt]{book}
@@ -34,7 +34,7 @@
 
 % Section: Overview
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 This document provides the reader with the information necessary to
@@ -88,7 +88,7 @@
 \end{itemize}
 
 Key publications reporting on and charting the development of the model are
-\cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99}:
+\cite{hill:95,marshall:97a,marshall:97b,adcroft:97,marshall:98,adcroft:99,hill:99,maro-eta:99,adcroft:04a,adcroft:04b,marshall:04}:
 
 \begin{verbatim}
 Hill, C. and J. Marshall, (1995)
@@ -137,12 +137,12 @@
 We begin by briefly showing some of the results of the model in action to
 give a feel for the wide range of problems that can be addressed using it.
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 \section{Illustrations of the model in action}
 
-The MITgcm has been designed and used to model a wide range of phenomena,
+MITgcm has been designed and used to model a wide range of phenomena,
 from convection on the scale of meters in the ocean to the global pattern of
 atmospheric winds - see figure \ref{fig:all-scales}. To give a flavor of the
 kinds of problems the model has been used to study, we briefly describe some
@@ -165,7 +165,7 @@
 
 Figure \ref{fig:eddy_cs} shows an instantaneous plot of the 500$mb$
 temperature field obtained using the atmospheric isomorph of MITgcm run at
-2.8$^{\circ }$ resolution on the cubed sphere. We see cold air over the pole
+$2.8^{\circ }$ resolution on the cubed sphere. We see cold air over the pole
 (blue) and warm air along an equatorial band (red). Fully developed
 baroclinic eddies spawned in the northern hemisphere storm track are
 evident. There are no mountains or land-sea contrast in this calculation,
@@ -210,16 +210,16 @@
 increased until the baroclinic instability process is resolved, numerical
 solutions of a different and much more realistic kind, can be obtained.
 
-Figure \ref{fig:ocean-gyres} shows the surface temperature and velocity 
-field obtained from MITgcm run at $\frac{1}{6}^{\circ }$ horizontal 
-resolution on a $lat-lon$
-grid in which the pole has been rotated by 90$^{\circ }$ on to the equator
-(to avoid the converging of meridian in northern latitudes). 21 vertical
-levels are used in the vertical with a `lopped cell' representation of
-topography. The development and propagation of anomalously warm and cold
-eddies can be clearly seen in the Gulf Stream region. The transport of
-warm water northward by the mean flow of the Gulf Stream is also clearly
-visible.
+Figure \ref{fig:ocean-gyres} shows the surface temperature and
+velocity field obtained from MITgcm run at $\frac{1}{6}^{\circ }$
+horizontal resolution on a \textit{lat-lon} grid in which the pole has
+been rotated by $90^{\circ }$ on to the equator (to avoid the
+converging of meridian in northern latitudes). 21 vertical levels are
+used in the vertical with a `lopped cell' representation of
+topography. The development and propagation of anomalously warm and
+cold eddies can be clearly seen in the Gulf Stream region. The
+transport of warm water northward by the mean flow of the Gulf Stream
+is also clearly visible.
 
 %% CNHbegin
 \input{part1/atl6_figure}
@@ -231,14 +231,14 @@
 <!-- CMIREDIR:global_ocean_circulation: -->
 \end{rawhtml}
 
-Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean currents at 
-the surface of a 4$^{\circ }$
-global ocean model run with 15 vertical levels. Lopped cells are used to
-represent topography on a regular $lat-lon$ grid extending from 70$^{\circ
-}N $ to 70$^{\circ }S$. The model is driven using monthly-mean winds with
-mixed boundary conditions on temperature and salinity at the surface. The
-transfer properties of ocean eddies, convection and mixing is parameterized
-in this model.
+Figure \ref{fig:large-scale-circ} (top) shows the pattern of ocean
+currents at the surface of a $4^{\circ }$ global ocean model run with
+15 vertical levels. Lopped cells are used to represent topography on a
+regular \textit{lat-lon} grid extending from $70^{\circ }N$ to
+$70^{\circ }S$. The model is driven using monthly-mean winds with
+mixed boundary conditions on temperature and salinity at the surface.
+The transfer properties of ocean eddies, convection and mixing is
+parameterized in this model.
 
 Figure \ref{fig:large-scale-circ} (bottom) shows the meridional overturning 
 circulation of the global ocean in Sverdrups.
@@ -301,14 +301,14 @@
 `automatic adjoint compiler'. These can be used in parameter sensitivity and
 data assimilation studies.
 
-As one example of application of the MITgcm adjoint, Figure \ref{fig:hf-sensitivity}
-maps the gradient $\frac{\partial J}{\partial \mathcal{H}}$where $J$ is the magnitude
-of the overturning stream-function shown in figure \ref{fig:large-scale-circ}
-at 60$^{\circ }$N and $
-\mathcal{H}(\lambda,\varphi)$ is the mean, local air-sea heat flux over
-a 100 year period. We see that $J$ is
-sensitive to heat fluxes over the Labrador Sea, one of the important sources
-of deep water for the thermohaline circulations. This calculation also
+As one example of application of the MITgcm adjoint, Figure
+\ref{fig:hf-sensitivity} maps the gradient $\frac{\partial J}{\partial
+  \mathcal{H}}$where $J$ is the magnitude of the overturning
+stream-function shown in figure \ref{fig:large-scale-circ} at
+$60^{\circ }N$ and $ \mathcal{H}(\lambda,\varphi)$ is the mean, local
+air-sea heat flux over a 100 year period. We see that $J$ is sensitive
+to heat fluxes over the Labrador Sea, one of the important sources of
+deep water for the thermohaline circulations. This calculation also
 yields sensitivities to all other model parameters.
 
 %%CNHbegin
@@ -341,14 +341,16 @@
 <!-- CMIREDIR:ocean_biogeo_cycles: -->
 \end{rawhtml}
 
-MITgcm is being used to study global biogeochemical cycles in the ocean. For
-example one can study the effects of interannual changes in meteorological
-forcing and upper ocean circulation on the fluxes of carbon dioxide and
-oxygen between the ocean and atmosphere. Figure \ref{fig:biogeo} shows 
-the annual air-sea flux of oxygen and its relation to density outcrops in 
-the southern oceans from a single year of a global, interannually varying 
-simulation. The simulation is run at $1^{\circ}\times1^{\circ}$ resolution
-telescoping to $\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not shown).
+MITgcm is being used to study global biogeochemical cycles in the
+ocean. For example one can study the effects of interannual changes in
+meteorological forcing and upper ocean circulation on the fluxes of
+carbon dioxide and oxygen between the ocean and atmosphere. Figure
+\ref{fig:biogeo} shows the annual air-sea flux of oxygen and its
+relation to density outcrops in the southern oceans from a single year
+of a global, interannually varying simulation. The simulation is run
+at $1^{\circ}\times1^{\circ}$ resolution telescoping to
+$\frac{1}{3}^{\circ}\times\frac{1}{3}^{\circ}$ in the tropics (not
+shown).
 
 %%CNHbegin
 \input{part1/biogeo_figure}
@@ -372,7 +374,7 @@
 \input{part1/lab_figure}
 %%CNHend
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 \section{Continuous equations in `r' coordinates}
@@ -409,11 +411,11 @@
 \input{part1/vertcoord_figure.tex}
 %%CNHend
 
-\begin{equation*}
+\begin{equation}
 \frac{D\vec{\mathbf{v}_{h}}}{Dt}+\left( 2\vec{\Omega}\times \vec{\mathbf{v}}
 \right) _{h}+\mathbf{\nabla }_{h}\phi =\mathcal{F}_{\vec{\mathbf{v}_{h}}}
 \text{ horizontal mtm} \label{eq:horizontal_mtm}
-\end{equation*}
+\end{equation}
 
 \begin{equation}
 \frac{D\dot{r}}{Dt}+\widehat{k}\cdot \left( 2\vec{\Omega}\times \vec{\mathbf{
@@ -611,9 +613,11 @@
 atmosphere)}  \label{eq:moving-bc-atmos}
 \end{eqnarray}
 
-Then the (hydrostatic form of) equations (\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) 
-yields a consistent set of atmospheric equations which, for convenience, are written out in $p$
-coordinates in Appendix Atmosphere - see eqs(\ref{eq:atmos-prime}).
+Then the (hydrostatic form of) equations
+(\ref{eq:horizontal_mtm}-\ref{eq:humidity_salt}) yields a consistent
+set of atmospheric equations which, for convenience, are written out
+in $p$ coordinates in Appendix Atmosphere - see
+eqs(\ref{eq:atmos-prime}).
 
 \subsection{Ocean}
 
@@ -666,7 +670,9 @@
 \phi (x,y,r)=\phi _{s}(x,y)+\phi _{hyd}(x,y,r)+\phi _{nh}(x,y,r)
 \label{eq:phi-split}
 \end{equation}
-and write eq(\ref{eq:incompressible}) in the form:
+%and write eq(\ref{eq:incompressible}) in the form: 
+%                  ^- this eq is missing (jmc) ; replaced with:
+and write eq( \ref{eq:horizontal_mtm}) in the form:
 
 \begin{equation}
 \frac{\partial \vec{\mathbf{v}_{h}}}{\partial t}+\mathbf{\nabla }_{h}\phi
@@ -766,15 +772,16 @@
 
 \subsubsection{Shallow atmosphere approximation}
 
-Most models are based on the `hydrostatic primitive equations' (HPE's) in
-which the vertical momentum equation is reduced to a statement of
-hydrostatic balance and the `traditional approximation' is made in which the
-Coriolis force is treated approximately and the shallow atmosphere
-approximation is made.\ The MITgcm need not make the `traditional
-approximation'. To be able to support consistent non-hydrostatic forms the
-shallow atmosphere approximation can be relaxed - when dividing through by $
-r $ in, for example, (\ref{eq:gu-speherical}), we do not replace $r$ by $a$,
-the radius of the earth.
+Most models are based on the `hydrostatic primitive equations' (HPE's)
+in which the vertical momentum equation is reduced to a statement of
+hydrostatic balance and the `traditional approximation' is made in
+which the Coriolis force is treated approximately and the shallow
+atmosphere approximation is made.  MITgcm need not make the
+`traditional approximation'. To be able to support consistent
+non-hydrostatic forms the shallow atmosphere approximation can be
+relaxed - when dividing through by $ r $ in, for example,
+(\ref{eq:gu-speherical}), we do not replace $r$ by $a$, the radius of
+the earth.
 
 \subsubsection{Hydrostatic and quasi-hydrostatic forms}
 \label{sec:hydrostatic_and_quasi-hydrostatic_forms}
@@ -811,7 +818,7 @@
 
 \subsubsection{Non-hydrostatic and quasi-nonhydrostatic forms}
 
-The MIT model presently supports a full non-hydrostatic ocean isomorph, but
+MITgcm presently supports a full non-hydrostatic ocean isomorph, but
 only a quasi-non-hydrostatic atmospheric isomorph.
 
 \paragraph{Non-hydrostatic Ocean}
@@ -1070,7 +1077,7 @@
 
 The mixing terms for the temperature and salinity equations have a similar
 form to that of momentum except that the diffusion tensor can be
-non-diagonal and have varying coefficients. $\qquad $
+non-diagonal and have varying coefficients.
 \begin{equation}
 D_{T,S}=\nabla .[\underline{\underline{K}}\nabla (T,S)]+K_{4}\nabla
 _{h}^{4}(T,S)  \label{eq:diffusion}
@@ -1096,8 +1103,9 @@
 
 \subsection{Vector invariant form}
 
-For some purposes it is advantageous to write momentum advection in eq(\ref
-{eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the (so-called) `vector invariant' form:
+For some purposes it is advantageous to write momentum advection in
+eq(\ref {eq:horizontal_mtm}) and (\ref{eq:vertical_mtm}) in the
+(so-called) `vector invariant' form:
 
 \begin{equation}
 \frac{D\vec{\mathbf{v}}}{Dt}=\frac{\partial \vec{\mathbf{v}}}{\partial t}
@@ -1118,7 +1126,7 @@
 Tangent linear and adjoint counterparts of the forward model are described
 in Chapter 5.
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 \section{Appendix ATMOSPHERE}
@@ -1208,6 +1216,7 @@
 surface ($\phi $ is imposed and $\omega \neq 0$).
 
 \subsubsection{Splitting the geo-potential}
+\label{sec:hpe-p-geo-potential-split}
 
 For the purposes of initialization and reducing round-off errors, the model
 deals with perturbations from reference (or ``standard'') profiles. For
@@ -1237,7 +1246,8 @@
 The final form of the HPE's in p coordinates is then: 
 \begin{eqnarray}
 \frac{D\vec{\mathbf{v}}_{h}}{Dt}+f\hat{\mathbf{k}}\times \vec{\mathbf{v}}
-_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} \label{eq:atmos-prime} \\
+_{h}+\mathbf{\nabla }_{p}\phi ^{\prime } &=&\vec{\mathbf{\mathcal{F}}} 
+\label{eq:atmos-prime} \\
 \frac{\partial \phi ^{\prime }}{\partial p}+\alpha ^{\prime } &=&0 \\
 \mathbf{\nabla }_{p}\cdot \vec{\mathbf{v}}_{h}+\frac{\partial \omega }{
 \partial p} &=&0 \\
@@ -1245,7 +1255,7 @@
 \frac{D\theta }{Dt} &=&\frac{\mathcal{Q}}{\Pi } 
 \end{eqnarray}
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 \section{Appendix OCEAN}
@@ -1283,8 +1293,9 @@
 _{\theta ,S}\frac{Dp}{Dt}  \label{EOSexpansion}
 \end{equation}
 
-Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is the
-reciprocal of the sound speed ($c_{s}$) squared. Substituting into \ref{eq-zns-cont} gives: 
+Note that $\frac{\partial \rho }{\partial p}=\frac{1}{c_{s}^{2}}$ is
+the reciprocal of the sound speed ($c_{s}$) squared. Substituting into
+\ref{eq-zns-cont} gives:
 \begin{equation}
 \frac{1}{\rho c_{s}^{2}}\frac{Dp}{Dt}+\mathbf{\nabla }_{z}\cdot \vec{\mathbf{
 v}}+\partial _{z}w\approx 0  \label{eq-zns-pressure}
@@ -1461,7 +1472,7 @@
 _{nh}=0$ form of these equations that are used throughout the ocean modeling
 community and referred to as the primitive equations (HPE).
 
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.19 2004/03/23 16:47:04 afe Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_overview/text/manual.tex,v 1.26 2006/06/28 15:22:13 edhill Exp $
 % $Name:  $
 
 \section{Appendix:OPERATORS}
@@ -1478,9 +1489,8 @@
 \end{equation*}
 
 \begin{equation*}
-v=r\frac{D\varphi }{Dt}\qquad
+v=r\frac{D\varphi }{Dt}
 \end{equation*}
-$\qquad \qquad \qquad \qquad $
 
 \begin{equation*}
 \dot{r}=\frac{Dr}{Dt}
@@ -1490,7 +1500,7 @@
 distance of the particle from the center of the earth, $\Omega $ is the
 angular speed of rotation of the Earth and $D/Dt$ is the total derivative.
 
-The `grad' ($\nabla $) and `div' ($\nabla $.) operators are defined by, in
+The `grad' ($\nabla $) and `div' ($\nabla\cdot$) operators are defined by, in
 spherical coordinates:
 
 \begin{equation*}
@@ -1500,7 +1510,7 @@
 \end{equation*}
 
 \begin{equation*}
-\nabla .v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial
+\nabla\cdot v\equiv \frac{1}{r\cos \varphi }\left\{ \frac{\partial u}{\partial
 \lambda }+\frac{\partial }{\partial \varphi }\left( v\cos \varphi \right) \right\}
 +\frac{1}{r^{2}}\frac{\partial \left( r^{2}\dot{r}\right) }{\partial r}
 \end{equation*}